A chemist needs 120 milliliters of a 33% solution but has only 13% and 73% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Answer:

5

Step-by-step explanation:

firstly, what are complementry angles.complementary angles are angles that su

m up to 90°

(12x-18)+(5x+23)=90

collecting like terms

12x+5x+23-18=90

17x-5-90=0

17x-95=0

17x=95

divide through by 17

x=5

The measure of the smaller angle when complementary angles are given is 42 degree.

Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.

The first angle of the triangle is (12x - 18).

The measure of the second angle of the triangle is (5x + 23).

As both angles are complementary, their sum would be equal to 90 degree.

(12x - 18) + (5x + 23) = 90

12x -  18 + 5x + 23 = 90

17x = 85

x = 5

Substitute the value of x = 5 in the given angles.

(1) 12x - 18 = 12×5 - 18

    = 42 degrees

(2) 5x + 23 = 5×5 +23

    = 48 degrees

Therefore, the smaller angle is found to be 42 degrees.  

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Answer:

∠CDE

Step-by-step explanation:

Name it by the order of the letters with the point of the angle in the middle

Answer:

1/3 feet.

Step-by-step explanation:

The length = area / width

= 7/9 / 2 1/3

= 7/9 / 7/3

= 7/9 * 3/7

= 3/9

= 1/3 feet,

Answer:

√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.

Answer:

[tex] 7\sqrt{3} [/tex]

Step-by-step explanation:

[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]

Answer:

n = 5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 30 = n/ 5 sqrt(3)

5 sqrt(3) tan 30 = n

5 sqrt(3) * 1/ sqrt(3) = n

5 = n

Answer:

C(x) = 0.2x^5 - x^2 + 6000

Step-by-step explanation:

Given in the question are restated as follows:

Marginal cos = C'(x) = x^4 - 2x ...................... (1)

Note that marginal cost (C'(x)) refers to the change in the total cost (C(x)) as a result of one more unit increase in the quantity produced. That is, MC refers to the additional cost incurred in order to produce one more unit of a good.

Therefore, TC can be obtained by integrating equation (1) as follows:

C(x) = ∫C'(x) = ∫[x^4 - 2x]dx

C(x) = 1/5x^5 - 2/2x^2 + F ................................ (2)

Where F is the fixed cost. Since the fixed cost is given as $6,000 in the question, we substitute it for F into equation (2) and solve as follows:

C(x) = 0.2x^5 - x^2 + 6000 ......................... (3)

Equation (3) is the total cost function​ C.

Answer:

Subtract the 2w to both sides of the equal sign.

Step-by-step explanation:

Since we want the equation to be in terms of l, we need to isolate the term first. To do so, we will need to subtract 2w on both sides to start out.

Answer:1.8(x -1)

2.0.4a -7

Step-by-step explanation:

Answer:

the answer is false

Step-by-step explanation:

FALSE. A person who yells at an official is not showing a competitive spirit.

A competitive spirit shows the following attributes:

A person yelling at an official is not a way of communicating respect. Therefore, it is FALSE to say it is a display of competitive spirit.

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Answer:

Step-by-step explanation:

I can help

Answer:

Step-by-step explanation:

Let the angle be x

To find the indicated angle we use sine

sin ∅ = opposite / hypotenuse

From the question

7 is the hypotenuse

4 is the opposite

sin x = 4/7

x = sin-¹ 4/7

x = 34.85

x = 35° to the nearest degree

Hope this helps you

Answer:  G ∩ M = {Anael, Max}

G U S = {Acel, Acton, Anael, Barek, Carl, Carlin, Dario, Kai, Max}

Step-by-step explanation:

intersection ∩ - items found in BOTH sets

union U - the joining of the sets. include EVERYTHING in the sets.

G = (Acel, Acton, Anael, Carl, Dario, Max}

S = {Anael, Barek, Bay, Carlin, Kai, Max}

G ∩ S: Anael and Max are found in both sets

G = (Acel, Acton, Anael, Carl, Dario, Max}

S = {Acton, Anael, Barek,  Carlin, Dario, Kai}

G U S: include everything in G and everything in S. If found in both sets, only list it once.

G U S = {Acel, Acton, Anael, Barek, Carl, Carlin, Dario, Kai, Max}

    Notice that Acton and Anael are in both sets but we only list them once.

The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.

For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.

(i) For x = 6.9:

mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)

= 2.22

(ii) For x = 6.99:

mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)

= 2.020

(iii) For x = 6.999:

mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)

= 2.002002

(iv) For x = 6.9999:

mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)

= 2.000200

(v) For x = 7.1:

mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)

= 1.818182

(vi) For x = 7.01:

mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)

= 1.980198

(vii) For x = 7.001:

mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)

= 1.998002

(viii) For x = 7.0001:

mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)

= 1.999800

By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.

Using the point-slope form, we have:

y - y₁ = m(x - x₁)

Substituting the values of P(7, -2), we have:

y - (-2) = 2(x - 7)

y = 2x -16

Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.

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Answer:

The correct answer is 5.5988 x [tex]10^{-3}[/tex] = 0.0055988

Explanation:

In mathematics and related areas, it is common the expression [tex]10^{n}[/tex] (n = a whole number) that multiplies a number, this is known as scientific notation, and it used to express long numbers concisely. This type of notation implies the exponent number or n represents the number of zeros in the number or the number of spaces after/before the decimal period.

Additionally, if the exponent is positive this means the zeros are placed to the right of the number, while a negative exponent shows the zeros are on the left. For example 7 x [tex]10^{3}[/tex] is equal to 7000 because the exponent indicates there are three zeros to the right of 7 or you need to move three spaces the period to the right, which is located right after 7. According to this, the expression 5.5988 x [tex]10^{-3}[/tex] indicates there are 3 zeros to the left of this number or that you need to move three spaces the period and add zeros in these spaces, which is equal to 0.0055988. Therefore, both numbers are equal (=)

Answer:

42°

Step-by-step explanation:

AD is a line

AEC and DEC are both 90°

AEB and CEB make up 90°

AEB+CEB=AEC substitute

AEB+48=90 Next use Subtraction property of equality

AEB=42

Hope this helps, if so please give me brainliest, it helps a lot. :)

Have a good day!

Answer:

∠AEB=42

Step-by-step explanation:

∠AEB and ∠BEC are inside of ∠AEC.

∠AEC is a right angle, Since ∠AEC and ∠CED are on a straight line, they must add to 180 degrees. ∠CED is a right angle (the little square in the corner tell us this), so ∠AEC must also be a right angle. This is because a right angle is 90 degrees (∠CED+∠AEC=180 --> 90+∠AEC=180 --> ∠AEC=90)

Therefore, the 2 angles (AEB and BEC) inside of ∠AEC must add to 90 degrees.

∠AEB+ ∠BEC= 90

We know that ∠BEC=48

∠AEB+48=90

We want to find out what ∠AEB is. We must get ∠AEB by itself. 48 is being added, and the inverse of addition is subtraction. Subtract 48 from both sides.

∠AEB+48-48=90-48

∠AEB=90-48

∠AEB=42

Answer:

1. -6.5x+11

2. 6b-5

3. 3p-5.1

Step-by-step explanation:

[tex]1. \\(x-1)+(12-7.5x)=\\x-1+12-7.5x=\\x-7.5x-1+12=\\-6.5x-1+12=\\-6.5x+11\\\\2.\\b-(4-2b)+(3b-1)=\\b-4+2b+3b-1=\\b+2b+3b-4-1=\\3b+3b-4-1=\\6b-4-1=\\6b-5\\\\3.\\(2p+1.9)-(7-p)=\\2p+1.9-7+p=\\2p+p+1.9-7=\\3p+1.9-7=\\3p-5.1[/tex]

Answer:

Step-by-step explanation:

There are two distinct statements but put together, it is:

- If Maria Cantwell (MC) promotes Alternative Energy (AE) and if Patty Murray (PM) supports Wilderness Areas (WA) then Dianne Feinstein (DF) advocating Gun Control (GC), implies that Susan Collins (SC) does so too.

For Susan Collins, she advocates gun control too.

So the symbolic or algebraic representation is:

(SC = DF): (MC ~ AE), (PM ~ WA)

OR

(GC = GC): (MC ~ AE), (PM ~ WA)

Where ":" represents "such that" or "given that"

" ~ " represents "support or promotion of"

It can now be read thus;

Susan Collins has same or equal interest as Dianne Feinstein, given that Maria Cantwell promotes alternative energy and Patty Murray supports Wilderness Areas.

Answer:

The answer is option A

4 x ( 9 + 6)

Hope this helps you

Answer:

[tex]\dfrac{1213}{9999}[/tex]

Step-by-step explanation:

We are required to express [tex]0.\overline{1}+0.\overline{01}+0.\overline{0001}[/tex] as a common fraction.

The bar on top of the decimal part indicates the decimal number is a repeating decimal.

Therefore:

[tex]0.\overline{1}=\dfrac{1}{10-1}= \dfrac{1}{9}\\\\0.\overline{01}=\dfrac{1}{100-1}= \dfrac{1}{99}\\\\0.\overline{0001}=\dfrac{1}{10000-1}= \dfrac{1}{9999}\\\\\\$Therefore$:\\0.\overline{1}+0.\overline{01}+0.\overline{0001} \\=\dfrac{1}{9}+\dfrac{1}{99}+\dfrac{1}{9999}\\\\=\dfrac{1213}{9999}[/tex]

Answer:

i think it might be A. 0.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

k = 3 ; 2k + 2 = 2*3 + 2 = 6 + 2 = 8

k = 4;  2k + 2 = 2*4 + 2 = 8 +2 = 10

k =5; 2k + 2 = 2*5 +2 = 10+2 = 12

k=6;  2k +2 = 2*6 + 2 = 12+2 = 14

k = 7 ; 2k + 2 = 2*7 +2 = 14 +2 = 16

k = 8 ; 2k + 2 = 2*8 + 2 = 16 +2 = 18

∑ (2k + 2) = 8 + 10 + 12 + 14 + 16 + 18 = 78

The answers are in order

r = −0.08 --> weak negative correlation

r = −0.83 --> strong negative correlation

r = 0.96 --> strong positive correlation

r = 0.06 --> weak positive correlation

The match of each correlation is given by,

r = −0.08  implies a weak negative correlation

r = −0.83  implies a strong negative correlation

r = 0.96  implies strong positive correlation

r = 0.06 implies  weak positive correlation.

We have given that,

The correlation coefficient, r, to its description.

A                                                 B

r = −0.08                             strong negative correlation

r = −0.83                               weak positive correlation                

r = 0.96                               weak negative correlation                    

r = 0.06                                strong positive correlation

We have to match the given relation

If the correlation coefficient is greater than zero, it is a positive relationship. Conversely, if the value is less than zero, it is a negative relationship.

So the correct match is,

r = −0.08  implies a weak negative correlation

r = −0.83  implies strong negative correlation

r = 0.96  implies strong positive correlation.

r = 0.06 is implies  weak positive correlation.

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Answer:

The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm

The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm

The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm

Answer:  19.5 miles or 108.75 miles

Step-by-step explanation:

Let ship traveled to the west x hours and then to the north y hours. Total 7 hours.  So we can write 1st equation

x+y=7                                                          (1)

The ship traveled to the west x hours with speed 25 miles/h - the distance 25*x

The ship traveled to the north y hours with speed 19 miles/hour - the distance   19*y

Note that the angle between north and west directions is 90 degrees.

So if the initial traveling point is A, the final travelling point ic C and the point ,  where ther the ship has changed the travelling direction from West to North is B.

So we have the right triangle ABC, where B angle is right=90 degrees.

AB side=25*x,  BC side= 19*y and AC side 145 miles.

According to Pithagor theorem we can write

AC^2=AB^2+BC^2

21025=625*x^2+ 361*y^2                       (2)

Solve the system of equations (1) and (2)

y=7-x

625*x^2+361*(7-x)^2=21025

625*x^2+361*(49-14x+x^2)=21025

625*x^2+17689-5054*x+361*x^2=21025

986*x^2- 5054*x-3336=0   dividing on 2 we'll get

493*x^2-2527*x-1668=0

D=3096433 sqrt(D)=appr 1760

x1=(2527-1760)/493/2= appr  0.78 h  

x2=(2527+1760)/493/2=appr 4.35 h  

So the problem has 2 solutions :

heading west the ship traveled  or 0.78*25= 19.5 miles

Or 4.35*25= 108.75 miles

Answer:

let w = time heading west at 25 mph

the total time is 7 hrs, therefore

(7-w) = time heading north at 19 mph

Distance = speed * time

25w + 19(7-w) = 145

25w + 133 - 19w = 145

25w - 19w = 145 - 133

6w = 12

w = 12/6

w = 2 hrs traveling west

therefore

2 * 25 = mile going west

Confirm this solution, 7 - 2 = 5 hrs going north

19 * 5 = 95mi

25 * 2 = 50mi

--------------

total dist 145 mi

Answer:

Step-by-step explanation:

The composite shape consists of a semi circle and a triangle. The formula for determining the perimeter of a semicircle is expressed as

Perimeter = 1/2 × 2πr = πr

Since radius, r = 3, then

Perimeter of semi circle = 3 × 3.14 = 9.42 inches

Perimeter of composite shape = 9.42 + 5 + 5 = 19.42 inches

Area of semi circle = 1/2 × πr²

Area of semicircle = 1/2 × 3.14 × 3² = 14.13 inches²

Area of triangle = 1/2 × base × height

Area of triangle = 1/2 × 6 × 4 = 12 inches²

Area of composite shape = 14.13 + 12 = 26.13 inches²

The perimeter and area of the composite shape is:

Recall:

Area of a circle = πr²

Perimeter of circle = 2πr

Area of triangle = 1/2(bh)

The composite shape given is composed of a triangle and a semicircle.

Perimeter of the composite shape = Perimeter of semicircle + the length of the two sides of the triangle

Perimeter = 1/2(2 × 3.14 × 3) + 2(5) = 19.42 inches

Area of the composite shape = area of semicircle + area of triangle

Area = 1/2(3.14 × 3²) + 1/2(6 × 4)

Are = 14.13 + 12

Area of the composite shape = 26.13 square inches.

Therefore, the perimeter and area of the composite shape is:

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Answer:

The  polar form  is  sinθ  = 2 r³cos⁴θ

Step-by-step explanation:

Explanation:-

Given function y = 2 x⁴

Parametric Form  x = r cosθ ....(i)

                     and y = r sinθ ....(ii)

            squaring  x² = r² cos ²θ

                            y² = r² sin²θ

         adding   x² +  y² = r² cos ²θ+r² s in²θ

                                    =  r²( cos ²θ+s in²θ)

                                   =  r²( 1)

                     x² +  y² =    r²

Given function y = 2 x⁴

Now convert into polar form

                        r sinθ  = 2 (r cos θ )⁴

                         r sinθ  = 2 (r )⁴cos θ )⁴

                           sinθ  = 2 r ³cos⁴θ

Answer: L = 20.25

Step-by-step explanation:

[tex]T=2\pi \sqrt{\dfrac{L}{32}}[/tex]

Given: T = 5, π = 22/7

[tex]5=2\bigg(\dfrac{22}{7}\bigg)\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{5}{2}\bigg(\dfrac{7}{22}\bigg)=\sqrt{\dfrac{L}{32}}\\\\\\\dfrac{35}{44}=\sqrt{\dfrac{L}{32}}\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\bigg(\sqrt{\dfrac{L}{32}}\bigg)^2\\\\\\\bigg(\dfrac{35}{44}\bigg)^2=\dfrac{L}{32}\\\\\\32\bigg(\dfrac{35}{44}\bigg)^2=L\\\\\\\large\boxed{20.25=L}[/tex]

Answer:

"Vx: if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Step-by-step explanation:

The Following statement in the form  âˆ€x ______, if _______ then _______ is a valid argument and this because any valid argument with "true premises" has a "true conclusion" as well

we will rewrite this statement in a universal condition statement form

assume x is a valid argument with true premises

then the following holds true

p(x) : x is a valid argument with true premises

q(x) : x has true conclusion

applying universal conditional statement

"Vx, if x is a valid argument with true premises then x has a true conclusion"

In a symbol form

Vx ( P(x) ⇒ 2(x) )

Answer:

b = 0

Step-by-step explanation:

The standard form of a regular quadratic equation is ax² + bx + c and the standard form of the difference of squares is ax² - c. This means that b = 0 because there is no x term.